A combinatorial view of Andrews' proof of the L-M-W conjectures
The authors provide combinatorial proofs of some identities already proved analytically by \textit{G. Andrews} [Partitions, q-series, and the Lusztig-Macdonald-Wall conjectures, Invent. Math. 41, 91-102 (1977; Zbl 0354.20006)]. The combinatorial setting is lattice paths which the authors say stems from formal language methods, most particularly the work of Flajolet and Viennot. (There are references given in the paper under review.) In fact, the procedure can be used to attack lattice path interpretations to sequences of polynomials defined by difference equations with polynomial coefficients. The authors indicate that their methods have many applications to problems dealing with the theory of partitions. No doubt, this paper is the first of a series in which interesting combinatorial interpretations are attached to partition identities. This paper should be studied by combinatorialists who work with generating functions.
scientific article; zbMATH DE number 3993592